This booklet takes an in-depth examine abelian kin of codimension one webs within the complicated analytic environment. In its classical shape, net geometry is composed within the examine of webs as much as neighborhood diffeomorphisms. an important a part of the idea revolves round the notion of abelian relation, a specific form of useful relation one of the first integrals of the foliations of an internet. major focuses of the e-book comprise what percentage abelian family members can an online hold and which webs are sporting the maximal attainable variety of abelian kin. The booklet deals entire proofs of either Chern’s sure and Trépreau’s algebraization theorem, together with the entire beneficial must haves that transcend easy advanced research or uncomplicated algebraic geometry. many of the examples recognized modern of non-algebraizable planar webs of maximal rank are mentioned intimately. A old account of the algebraization challenge for maximal rank webs of codimension one can also be presented.

This small publication has for a very long time been a special position to discover classical effects from geometry, corresponding to Pythagoras' theorem, the nine-point circle, Morley's triangle, Poncelet's polygons, and plenty of different topics. additionally, this booklet includes contemporary, geometric theorems that have been got during this classical box during the last years.

With thousands of labored examples, workouts and illustrations, this targeted exposition of the speculation of Vassiliev knot invariants opens the sector to scholars with very little wisdom during this zone. It additionally serves as a consultant to extra complicated fabric. The ebook starts with a simple and casual creation to knot idea, giving many examples of knot invariants earlier than the category of Vassiliev invariants is brought.

This booklet is an exposition of semi-Riemannian geometry (also known as pseudo-Riemannian geometry)--the examine of a gentle manifold supplied with a metric tensor of arbitrary signature. The relevant unique instances are Riemannian geometry, the place the metric is optimistic sure, and Lorentz geometry. for a few years those geometries have built nearly independently: Riemannian geometry reformulated in coordinate-free style and directed towards worldwide difficulties, Lorentz geometry in classical tensor notation dedicated to normal relativity.